Infinitary operations on C(X)

Infinitary operations on C(X)

[Michael Barr]

Way back, John Isbell told me that the theory of C*-algebras could
be dnoe with a batch of finitary operations such as convex sum, product,
and maybe others plus exactly one omega-ary operation that takes {x_i} to
\sum 2^{-i}x_i.  Does anyone know if John ever published this and where?

Michael


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Re: Infinitary operations on C(X)

[Andrew Stacey]

On Mon, May 03, 2010 at 03:18:57PM -0400, Michael Barr wrote:
> Way back, John Isbell told me that the theory of C*-algebras could
> be dnoe with a batch of finitary operations such as convex sum, product,
> and maybe others plus exactly one omega-ary operation that takes {x_i} to
> \sum 2^{-i}x_i.  Does anyone know if John ever published this and where?
>

Yes he did.

@article{MR686798,
	title = {Generating the algebraic theory of {$C(X)$}},
	author = {Isbell, John},
	eprint = {http://dx.doi.org/10.1007/BF02483718},
	fjournal = {Algebra Universalis},
	issn = {0002-5240},
	journal = {Algebra Universalis},
	mrclass = {08A65 (03G25 03G30 18C10)},
	mrnumber = {MR686798 (84e:08004)},
	mrreviewer = {A. Kh. Kushkule{\u\i}},
	pages = {153-155},
	url = {http://dx.doi.org/10.1007/BF02483718},
	volume = {15},
	year = {1982},
	}

The operations are laid out: the unit, multiplication by -1, multiplication,
a funny not-quite-doubling operation (x -> (2x v 1) n (-1)), and the one you
mention above.

(I learnt about this from the references of the paper by Pelletier and
Rosicky, MR1223636)

Andrew


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Re: Infinitary operations on C(X)

[Jiri Rosicky]

John Isbell published
Generating the algebraic theory of C(X), Alg. Univ. 15 (1982), 153-155
With Joan Pelletier, we wrote
Generating the monadic theory of C*-algebras and related categories,
Proc. Categ. Top. and Appl., World-Scientific 1989, 163-180;
On the equational theory of C*-algebras, Alg. Univ. 30 (1993), 275-284.
Jiri Rosicky

----- Forwarded message from Michael Barr <barr@math.mcgill.ca> -----

> Date: Mon, 3 May 2010 15:18:57 -0400 (EDT)
> From: Michael Barr <barr@math.mcgill.ca>
> To: Categories list <categories@mta.ca>
> Subject: categories: Infinitary operations on C(X)
>
> Way back, John Isbell told me that the theory of C*-algebras could
> be dnoe with a batch of finitary operations such as convex sum, product,
> and maybe others plus exactly one omega-ary operation that takes {x_i} to
> \sum 2^{-i}x_i.  Does anyone know if John ever published this and where?
>
> Michael
>
>
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

----- End forwarded message -----


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